RESPONSE: The problem with Lowder’s position is that is it self-defeating, and his probability estimate is not meaningful since he agrees that we do not know the intentions of God (predictively) with respect to resurrecting people on earth (including Jesus), he can’t turn around and use the estimated population of human beings to arrive at the prior improbability he does unless he knows that God has designed a well-defined random experiment of trial resurrection events wherein human beings constitute God’s sample space; this requires a highly detailed and specific knowledge of Gods intentions that is not only unavailable to Lowder, but is so specific in comparison to the question ‘would God want to raise Jesus from the dead’ that it is very difficult to see how Lowder can consistently say that we don’t know that God would want to do the latter, but he knows (he presupposes this part) that God is performing some sort of Bernoulli trial on Earth in the case of the former!? Moreover, even if Lowder knew this, his prior probability calculation illegitimately includes all humans up to the present wherein he would only be justified in using the total number of ‘trials’ up unto the point under consideration, namely, the resurrection of Jesus. So, what percentage of the total population had live and died up until the time of Jesus? Only 2 percent! So, using the figures Lowder does, we just need to find what 2 percent of the number he uses is which comes out to: ~2140000000, or approximately 2.14x 10^-9. This may still sound like a large number, but it would be 'weak sauce' for something like the case the McGrew's make for the resurection to overcome. But as I say, Lowder's calculation is not a meaningful probability. Let me say that I think Lowder's basic point would be legitimate if the hypothesis under consideration was that 'Jesus rose naturally, and randomly from the dead.' That is highly improbable in terms of frequency. But the hypothesis is not that Jesus rose naturally from the dead, it is that God raised Jesus supernaturally from the dead. THE BOTTOM LINE: Frequency probabilities are grossly unreliable when a personal agent is the causal explanation under consideration and what Lowder should focus on (which he does in his other Bayesian arguments) is epistemic probability and try to show that the prior probability of God existing and God wanting to raise Jesus from the dead is low; so probability in terms of frequency is misguided whereas the use of epistemic probability is not.

*Even if I am wrong about this, then skip down to point 6 below where I think the death knell for this objection rings loudly

4) Yet another avenue to explore in responding to this objection (of needing to know that God would want to raise Jesus from the dead) is to explore the relationship between Bayes Theorem, Inference to the Best Explanation, and Prior Probabilities. For example, William Lane Craig utilizes IBE instead of Bayes Theorem in his case for the resurrection because he says, the prior probability that God would want to raise Jesus from the dead is inscrutable, and so, he thinks, he doesn't even have to address this worry since he uses IBE. Does this response work? I think it does if one or both of the following relationships between Bayes, IBE, and prior probabilities is correct:

---- "Several authors have recently argued that not only is abduction compatible with Bayesianism, it is a much-needed supplement to it. The so far fullest defense of this view has been given by Lipton (2004, Ch. 7); as he puts it, Bayesians should also be “explanationists” (his name for the advocates of abduction). (For other defenses, see Okasha 2000, McGrew 2003, and Weisberg 2009.)... This is where, according to Lipton, abduction comes in. In his proposal, Bayesians ought to determine their prior probabilities and, if applicable, likelihoods on the basis of explanatory considerations...Whatever exact priors you are going to assign, you should assign a higher one to the hypothesis that explains the available data best than to any of its rivals (provided there is a best explanation)...The answer to the question of how explanatory considerations are to guide one's choice of priors would then presumably be that one ought to assign a higher prior to the best explanation than to its rivals, if this is not what one already does. If it is, one should just keep doing what one is doing... Another suggestion about the connection between abduction and Bayesian reasoning—to be found in Okasha 2000, McGrew 2003, and Lipton 2004 (Ch. 7)—is that the explanatory considerations may serve as a heuristic to determine, even if only roughly, priors and likelihoods in cases in which we would otherwise be clueless and could do no better than guessing. This suggestion is sensitive to the well-recognized fact that we are not always able to assign a prior to every hypothesis of interest, or to say how probable a given piece of evidence is conditional on a given hypothesis. Consideration of that hypothesis' explanatory power might then help us to figure out, if perhaps only within certain bounds, what prior to assign to it, or what likelihood to assign to it on the given evidence (SEP)."

----"Finally, a possibility that has so far not been considered in the literature is that abduction and Bayesianism do not so much work in tandem—as they do on the above proposals—as operate in different modes of reasoning; the Bayesian and the explanationist are characters that feature in different plays, so to speak. It is widely accepted that sometimes we speak and think about our beliefs in a categorical manner, while at other times we speak and think about them in a graded way. It is far from clear how these different ways of speaking and thinking about beliefs—the epistemology of belief and the epistemology of degrees of belief, to use Richard Foley's (1992) terminology—are related to one another. In fact, it is an open question whether there is any straightforward connection between the two, or even whether there is a connection at all. Be that as it may, given that the distinction is undeniable, it is a plausible suggestion that, just as there are different ways of talking and thinking about beliefs, there are different ways of talking and thinking about the revision of beliefs. In particular, abduction could well have its home in the epistemology of belief, and be called upon whenever we reason about our beliefs in a categorical mode, while at the same time Bayes' rule could have its home in the epistemology of degrees of belief. Hard-nosed Bayesians may insist that whatever reasoning goes on in the categorical mode must eventually be justifiable in Bayesian terms, but this presupposes the existence of bridge principles connecting the epistemology of belief with the epistemology of degrees of belief—and, as mentioned, whether such principles exist is presently unclear (SEP)."

5) Perhaps the best response in terms of not having to rely on the truth of auxillary hypotheses is simply to admit that the prior probability that God would want to raise Jesus from the dead is inscrutable, and since we have no additional reasons to think it is low (I have responsed to ex-apologists argument already; and recall, if Swinburne is correct, it may actually not be inscrutable and greater than 1/2), and we have good specific evidence for the resurrection (and the assumption that there aren't any equally good natural explanations is correct) , then we could simply assign the two hypotheses: 1-God would want to raise Jesus from the dead, and 2-God would not want to raise Jesus from the dead an objective and equal prior probability of .5 based on the prinicple of indifference and rationally conclude that God raised Jesus from the dead if that hypothesis has greater explanatory power than hypothesis 1 above since it follows immediately from this ratio :

P(E/H) P(E)

and Bayes's Theorem that of two hypotheses with equal priors, the one with greater explanatory power will have the greater posterior probability.

6) Cavin Colombetti argue that plausibility is the same thing as prior probability (starting on slide 380 here):

But then, the religio-historical context is what makes the resurrection hypothesis plausible, which by C & C's own lights makes it the case that the prior probability is not low anymore. Of course C & C are aware of this move and try to refute the appeal to the religio-historical context making the resurrection plausible by saying that the religio-historical context simply DOESN'T EXIST! starting on slide 337 and ending on slide 351. The only problem here is that they focus on things which they call dogmas of faith such as: the sinless life of Jesus, that Jesus died for our sins, that Jesus was God incarnate, etc. (which may or not have evidence in their favor) and ignore what proponents of the resurrection hypothesis actually say about what featurs of the religio-historical context make the resurrection plausible and how they know this (e.g. Craig, Licona, etc.): ..."This is extremely important, for a miracle without a context is inherently ambiguous. But in the case of Jesus' miracles and resurrection the context is religiously significant: they occur in the context of and as the climax to Jesus' own unparalleled life, teaching, and personal claim to authority, and served as signs of the inbreaking of the Kingdom."

Prior probability is assessed according to the data you allow. I don't recall my exact words in the dialogue with Prof Martin. But I'd say that given (a) evidence for God's existence, (b) the historicity of Jesus' predictions pertaining to his imminent death and resurrection, (c) his unique claims about himself, and (d) that he performed deeds that astonished crowds and that he regarded as divine miracles and exorcisms [c & d are not disputed by scholars], these, in my opinion, create a context charged with religious significance, i.e., a context in which we might expect a god to act. Thus, I do see a degree of plausibility to the resurrection hypothesis, which bears a resemblance to prior probability in Bayes' Theorem. I don't think Bayes' Theorem is appropriate for historical investigation for a number of reasons. And at present, historians don't employ it in their work.

I hope this helps.

Very Truly Yours,

Mike

THESE THINGS ABOUT THE RELIGIO-HISTORICAL CONTEXT ARE ACCEPTED BY the majority of NT scholars (except for (b) above). They are not 'dogmas of faith', but rather are open to the tools and methods of historical investigation and are firmly established as historical facts. So, contra C & C, if plausibility is the same thing as prior probability, and since the religio-historical context does exist, then it follows that the prior probability of God wanting to raise Jesus from the dead is not astronomically low, but in fact, it is plausible. Indeed, as Craig pointed out in his debate with Cavin, even the Jesus Seminar accepts the pertinent facts that go toward establishing a 'robust' religio-historical context.